Statistics and Probability Commons^™

Implementing The Use Of Personal Activity Data In An Introductory Statistics Course, Lacy Christensen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Integrating real data into a classroom is one of the recommendations in the Guidelines for Assessment and Instruction in Statistics Education (GAISE) college report which lays out guidelines for an introductory statistics course (Committee, GAISE College Report ASA Revision, 2016). In order to assess the effect of using real data in a classroom, the students received physical activity trackers to wear during an undergraduate introductory statistics course taught in the summer. This tracker, a Fitbit, enabled students to monitor and record their steps, calories, and active time throughout the class. Collecting personal activity data (PAD) creates a large database which …

Novel Statistical Models For Quantitative Shape-Gene Association Selection, Xiaotian Dai

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Other research reported that genetic mechanism plays a major role in the development process of biological shapes. The primary goal of this dissertation is to develop novel statistical models to investigate the quantitative relationships between biological shapes and genetic variants. However, these problems can be extremely challenging to traditional statistical models for a number of reasons: 1) the biological phenotypes cannot be effectively represented by single-valued traits, while traditional regression only handles one dependent variable; 2) in real-life genetic data, the number of candidate genes to be investigated is extremely large, and the signal-to-noise ratio of candidate genes is expected …

Extracting And Visualizing Data From Mobile And Static Eye Trackers In R And Matlab, Chunyang Li

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Eye tracking is the process of measuring where people are looking at with an eye tracker device. Eye tracking has been used in many scientific fields, such as education, usability research, sports, psychology, and marketing. Eye tracking data are often obtained from a static eye tracker or are manually extracted from a mobile eye tracker. Visualization usually plays an important role in the analysis of eye tracking data. So far, there existed no software package that contains a whole collection of eye tracking data processing and visualization tools. In this dissertation, we review the eye tracking technology, the eye tracking …

Exact Approaches For Bias Detection And Avoidance With Small, Sparse, Or Correlated Categorical Data, Sarah E. Schwartz

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Every day, traditional statistical methodology are used world wide to study a variety of topics and provides insight regarding countless subjects. Each technique is based on a distinct set of assumptions to ensure valid results. Additionally, many statistical approaches rely on large sample behavior and may collapse or degenerate in the presence of small, spare, or correlated data. This dissertation details several advancements to detect these conditions, avoid their consequences, and analyze data in a different way to yield trustworthy results.

One of the most commonly used modeling techniques for outcomes with only two possible categorical values (eg. live/die, pass/fail, …

Application Of Machine Learning And Statistical Learning Methods For Prediction In A Large-Scale Vegetation Map, Carla M. Brookey

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Original analyses of a large vegetation cover dataset from Roosevelt National Forest in northern Colorado were carried out by Blackard (1998) and Blackard and Dean (1998; 2000). They compared the classification accuracies of linear and quadratic discriminant analysis (LDA and QDA) with artificial neural networks (ANN) and obtained an overall classification accuracy of 70.58% for a tuned ANN compared to 58.38% for LDA and 52.76% for QDA.

Because there has been tremendous development of machine learning classification methods over the last 35 years in both computer science and statistics, as well as substantial improvements in the speed of computer hardware, …

A Comparison Of Five Statistical Methods For Predicting Stream Temperature Across Stream Networks, Maike F. Holthuijzen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The health of freshwater aquatic systems, particularly stream networks, is mainly influenced by water temperature, which controls biological processes and influences species distributions and aquatic biodiversity. Thermal regimes of rivers are likely to change in the future, due to climate change and other anthropogenic impacts, and our ability to predict stream temperatures will be critical in understanding distribution shifts of aquatic biota. Spatial statistical network models take into account spatial relationships but have drawbacks, including high computation times and data pre-processing requirements. Machine learning techniques and generalized additive models (GAM) are promising alternatives to the SSN model. Two machine learning …

A Tournament Approach To Price Discovery In The Us Cattle Market, Jeffrey Wright

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Cattle price discovery is a process of determining the price in the market through the interactions of cattle buyers (packers) and sellers (ranchers). Locating the price discovery center or market, and estimating price interactions among the regional fed cattle markets and also among feeder cattle markets can help define a relevant fed cattle procurement market. This research identifies that the U.S. cattle markets is discovered in the futures markets, feeder cattle futures and fed futures.

Combinatorial Games On Graphs, Trevor K. Williams

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Combinatorial Games are intriguing and have a tendency to engross students and lead them into a serious study of mathematics. The engaging nature of games is the basis for this thesis. Two combinatorial games and some educational tools are presented which were developed by the author in the pursuit of the solution of these games.

Separation Of Points And Interval Estimation In Mixed Dose-Response Curves With Selective Component Labeling, Darl D. Flake Ii

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Dose-response experiments are those that involve giving subjects different amounts of a treatment and observing the outcome. For example, plants may be given fertilizer and their growth could be measured or cancer patients could be given different doses of chemotherapy and their response could be monitored. These experiments are used to understand the relationship between the amount of, and response to, the treatment. Logistic regression models are often used to summarize data from these types of experiments. The dose-response experiment that motivated this dissertation involved treating a grain-pest with a pesticide. Some of the beetles had genes that made them …

To Dot Product Graphs And Beyond, Sean Bailey

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We will introduce three new vector representations of graphs. These representations are based on relationships between the vectors that are used. Specifically, we will examine scenarios where we ignore specific relationships, where we consider if information is missing, and where we look for when the information in common is not of a specified amount.

Bayesian Models For Repeated Measures Data Using Markov Chain Monte Carlo Methods, Yuanzhi Li

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Bayesian models for repeated measures data are fitted to three different data an analysis projects. Markov Chain Monte Carlo (MCMC) methodology is applied to each case with Gibbs sampling and/or an adaptive Metropolis-Hastings (MH) algorithm used to simulate the posterior distribution of parameters. We implement a Bayesian model with different variance-covariance structures to an audit fee data set. Block structures and linear models for variances are used to examine the linear trend and different behaviors before and after regulatory change during year 2004-2005. We proposed a Bayesian hierarchical model with latent teacher effects, to determine whether teacher professional development (PD) …

Modeling Seed Dispersal And Population Migration Given A Distribution Of Seed Handling Times And Variable Dispersal Motility: Case Study For Pinyon And Juniper In Utah, Ram C. Neupane

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The spread of fruiting tree species is strongly determined by the behavior and range of fruit-eating animals, particularly birds. Birds either consume and digest seeds or carry and cache them at some distance from the source tree. These carried and settled seeds provide some form of distribution which generates tree spread to the new location. Firstly, we modal seed dispersal by birds and introduce it in a dispersal model to estimate seed distribution. Using this distribution, we create a population model to estimate the speed at which juniper and pinyon forest boundaries move.

Secondly, we introduce a fact that bird …

Annotation Tools For Multivariate Gene Set Testing Of Non-Model Organisms, Russell K. Banks

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Microarray chip technology enables researchers to obtain measures of gene activity for essentially all genes in an organism. After grouping genes into biologically meaningful sets, researchers employ certain statistical tests to identify which gene sets (biological processes) show different levels of activity across different treatment groups. The idea is to identify which biological processes are significantly affected by a certain treatment/condition in a given organism.

Non-model organisms (such as sheep) are not widely studied so gene set membership information is not always readily accessible. This thesis work utilizes two microarray studies involving sheep to provide researchers with working examples of …

Family-Wise Error Rate Control In Quantitative Trait Loci (Qtl) Mapping And Gene Ontology Graphs With Remarks On Family Selection, Garrett Saunders

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One of the great aims of statistics, the science of collecting, analyzing, and interpreting data, is to protect against the probability of falsely rejecting an accepted claim, or hypothesis, given observed data stemming from some experiment. This is generally known as protecting against a Type I Error, or controlling the Type I Error rate. The extension of this protection against Type I Errors to the situation where thousands upon thousands of hypotheses are examined simultaneously is known as multiple hypothesis testing. This dissertation presents an improvement to an existing multiple hypothesis testing approach, the Focus Level method, specific to gene …

Family-Wise Error Rate Control In Quantitative Trait Loci (Qtl) Mapping And Gene Ontology Graphs With Remarks On Family Selection, Garrett Saunders

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One of the great aims of statistics, the science of collecting, analyzing, and interpreting data, is to protect against the probability of falsely rejecting an accepted claim, or hypothesis, given observed data stemming from some experiment. This is generally known as protecting against a Type I Error, or controlling the Type I Error rate. The extension of this protection against Type I Errors to the situation where thousands upon thousands of hypothesis are examined simultaneously is known as multiple hypothesis testing. This dissertation presents an improvement to an existing multiple hypothesis testing approach, the Focus Level method, specific to gene …

Beetles, Fungi And Trees: A Story For The Ages? Modeling And Projecting The Multipartite Symbiosis Between The Mountain Pine Beetle, Dendroctonus Ponderosae, And Its Fungal Symbionts, Grosmannia Clavigera And Ophiostoma Montium, Audrey L. Addison

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

As data collection and modeling improve, ecologists increasingly discover that interspecies dynamics greatly affect the success of individual species. Models accounting for the dynamics of multiple species are becoming more important. In this work, we explore the relationship between mountain pine beetle (MPB, Dendroctonus ponderosae Hopkins) and two mutualistic fungi, Grosmannia clavigera and Ophiostoma montium. These species are involved in a multipartite symbiosis, critical to the survival of MPB, in which each species benefits.

Extensive phenological modeling has been done to determine how temperature affects the timing of life events and cold-weather mortality of MPB. The fungi have also …

Computational Topics In Lie Theory And Representation Theory, Thomas J. Apedaile

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The computer algebra system Maple contains a basic set of commands for working with Lie algebras and matrices. The purpose of this thesis was to extend the functionality of these Maple packages in a number of important areas. First, programs for defining multiplication in several different types of algebras were created to allow users to perform a wider variety of calculations. Second, commands were created for calculating some basic properties of matrix representations of semisimple Lie algebras. This allows a user to identify a given matrix representation by a collection of integers which do not change when the basis of …

Physically Based Preconditioning Techniques Applied To The First Order Particle Transport And To Fluid Transport In Porous Media, Michael Rigley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Solving linear systems is at the heart of many scientific applications from the PreAlgebra's student solving for x and y for basic geometry problems to the computational scientist solving billions of equations with billions of variables for weather forecasting, modeling fusion reactions, or web search algorithms. In this study we look at improving the efficiency of solving large linear systems that result from two applications. The first includes linear systems that result from solving differential equations for the movement of atomic particles in particle emitting, void, and absorbing regions. The second includes solving linear systems that result from solving differential …

Implementation And Application Of The Curds And Whey Algorithm To Regression Problems, John Kidd

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A common statistical problem is trying to predict two or more variables using a set of predictor variables. The simplest model for this situation is called multivariate linear regression. This method uses each set of predictor variables to predict each of the response variables separately. This approach seems counter-intuitive as any possible relationship between the variables being predicted is ignored.

Breiman and Friedman found a way to take advantage of relationships among the response variables to increase the accuracy of the predictions for each of the predicted variables with an algorithm they called Curds and
Whey. It uses other statistical …

Statistical Modeling, Exploration, And Visualization Of Snow Water Equivalent Data, James Beguah Odei

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Due to a continual increase in the demand for water as well as an ongoing regional drought, there is an imminent need to monitor and forecast water resources in the Western United States. In particular, water resources in the Intermountain West rely heavily on snow water storage. Thus, the need to improve seasonal forecasts of snowpack and considering new techniques would allow water resources to be more effectively managed throughout the entire water-year. Many available models used in forecasting snow water equivalent (SWE) measurements require delicate calibrations.

In contrast to the physical SWE models most commonly used for forecasting, we …

Enhancement Of Random Forests Using Trees With Oblique Splits, Andrejus Parfionovas

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Statistical classification is widely used in many areas where there is a need to make a data-driven decision, or to classify complicated cases or objects. For instance: disease diagnostics (is a patient sick or healthy, based on the blood test results?); weather forecasting (will there be a storm tomorrow, based on today's atmospheric pressure, air temperature, and wind velocity?); speech recognition (what was said over the phone, based on the caller's voice level and articulation); spam detection (can the unsolicited commercial e-mails be identified by their content?); and so on.

Classification trees …

Statistical Algorithms For Optimal Experimental Design With Correlated Observations, Chang Li

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The first part of my dissertation demonstrates that a modified simulated annealing algorithm can successfully determine highly efficient D-optimal designs for second order polynomial regression for a variety of correlated error structures.

In the second part, I solved weak universal optimal block designs for the nearest neighbor correlation structure and multiple block sizes, for the hub correlation structure with any block size, and for circulant correlation with odd block size.

In the third part, we propose an improved Particle Swarm Optimization (PSO) algorithm with time varying parameters. Then combining the theorem of decision making and PSO, we innovated nested PSO …

Spatially Indexed Functional Data, Oleksandr Gromenko

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The increased concentration of greenhouse gases is associated with the global warming in the lower troposphere. For over twenty years, the space physics community has studied a hypothesis of global cooling in the thermosphere, attributable to greenhouse gases. While the global temperature increase in the lower troposphere has been relatively well established, the existence of global changes in the thermosphere is still under investigation.

A central difficulty in reaching definite conclusions is the absence of data with sufficiently long temporal and sufficiently broad spatial coverage. Time series of data that cover several decades exist only in a few separated (industrialized) …

Applications Of Bayesian Statistics In Fluvial Bed Load Transport, Mark L. Schmelter

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The science of fluvial sediment transport studies the processes involved in the movement of river sediments. It is commonly understood that when rivers flood they have a great capacity to move sand, gravel, and even larger cobbles and boulders. This process is not only limited to the big floods that usually attract so much attention, but also the more common river flows play a very important role in forming a river. As engineers and scientists, we like to be able to develop equations and relationships that describe some natural phenomenon—in this case, fluvial sediment transport. While we are able to …

Empirical Properties Of Functional Regression Models And Application To High-Frequency Financial Data, Xi Zhang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Functional data analysis (FDA) has grown into a substantial field of statistical research, with new methodology, numerous useful applications and interesting novel theoretical developments. My dissertation focuses on the empirical properties of functional regression models and their application to financial data. We start from testing the empirical properties of forecasts with the functional autoregressive models based on simulated and real data. We define intraday returns and consider their prediction from such returns on a market index. This is an extension to intraday data of the Capital Asset Pricing model. Finally we investigate multifactor functional models and assess their suitability for …

Existence And Multiplicity Results On Standing Wave Solutions Of Some Coupled Nonlinear Schrodinger Equations, Rushun Tian

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Coupled nonlinear Schrodinger equations (CNLS) govern many physical phenomena, such as nonlinear optics and Bose-Einstein condensates. For their wide applications, many studies have been carried out by physicists, mathematicians and engineers from different respects. In this dissertation, we focused on standing wave solutions, which are of particular interests for their relatively simple form and the important roles they play in studying other wave solutions. We studied the multiplicity of this type of solutions of CNLS via variational methods and bifurcation methods.

Variational methods are useful tools for studying differential equations and systems of differential equations that possess the so-called variational …

Visual Data Mining Techniques For Functional Actigraphy Data: An Object-Oriented Approach In R, Abbass Sharif

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Actigraphy, a technology for measuring a subject's overall activity level almost continuously over time, has gained a lot of momentum over the last few years. An actigraph, a watch-like device that can be attached to the wrist or ankle of a subject, uses an accelerometer to measure human movement every minute or even every 15 seconds. Actigraphy data is often treated as functional data. In this dissertation, we discuss what has been done regarding the visualization of actigraphy data, and then we will explain the three main goals we achieved: (i) develop new multivariate visualization techniques for actigraphy data; (ii) …

Robust Computational Tools For Multiple Testing With Genetic Association Studies, William L. Welbourn Jr.

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The mapping of the human genome and the completion of the Human HapMap project over the past decade have significantly altered how research is conducted with respect to the genetic epidemiology of human disease. Study designs and analytic approaches have evolved rapidly from investigations involving relatively few targeted candidate genes to hypothesis-free genome-wide association studies, where thousands – and now even millions – of single molecular mutations are simultaneously analyzed to identify regions of the genome that may influence disease. As laboratory techniques continue to improve and costs decrease, the volume of genetic data will inexorably rise, and robust tools …

Examining Child Sexual Abuse And Future Parenting: An Application Of Latent Class Modeling, Kimberly W. D'Zatko

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This study was designed to empirically derive latent classes of mothers who were sexually abused during childhood and to assess the association between depression, alcohol/drug use, supportive intimate partner, and specific classes.

One hundred six women between the ages of 20 and 44 years (M = 27) who reported having been sexually abused during childhood (CSA) and 158 non-CSA mothers between the ages of 20 and 43 years (M = 23) were interviewed and assessed along six parenting dimensions. Logistic regression models evaluated the association between psychoemotional variables and specific classes.

The final model consisted of three classes—53.2%, …

Psychometric Properties Of Postsecondary Students' Course Evaluations, Michael J. Drysdale

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Several experts in the area of postsecondary student evaluations of courses have concluded that they are stable or reliable measures as well as being measures that provide ways of making valid inferences regarding teacher effectiveness. Often these experts have offered these conclusions without supporting evidence. Surprisingly, a thorough review of the literature revealed very few reported test-retest reliability studies of course evaluations and the results from these studies are contradictory. In the area of validity, the conclusions offered by scholars who conducted meta-analyses of mutlisection course studies are inconsistent. This leads to the following two research questions:

1. What is …